Flexural behaviour of cementitious composites embedded with 3D printed re-entrant chiral auxetic meshes

3D printed auxetic metamaterials can be used to make high performing cementitious composites to strengthen existing structures and elements due to their negative Poisson’s ratio behaviour and high energy absorbing characteristics. In this paper, three different re-entrant chiral auxetic (RCA) meshes of various cell geometries and orientations were developed by 3D printing them using poly-lactic acid (PLA) and thermoplastic polyurethane (TPU) filament. The developed meshes were tested under out-of-plane flexure to study their load carrying capacity, ductility and energy absorption characteristics, especially to characterise the best cell orientation. The horizontal cells provided enhanced load carrying and energy absorption characteristics for all three cell geometries for both materials. These RCA meshes were then embedded into low and high strength premix cement mortar matrices to develop auxetic cementitious composites (ACCs). In total, 42 ACC specimens were casted and tested under flexural loading. The results were studied in terms of their failure patterns, load-displacement responses, flexural capacities, ductility and energy absorption. The RCA meshes made of PLA filament showed limited capacity and energy absorption as compared to RCA meshes made of TPU filament due to extended flexibility and resilience provided by TPU meshes. The RCA meshes with a denser cell structure exhibited highest flexural capacity and effective energy absorption of 14 700 kJ m−2 for TPU-RCA mesh embedded into high strength cement mortar matrix. The results obtained in this study have enabled to understand the flexural behaviour of cementitious composites embedded with 3D printed auxetic lattices and to strengthen the existing structures.


Introduction
Auxetic materials and composites have been used in defence, sports and machine vibration damping applications to improve mechanical and energy absorbing characteristics due to their unique negative Poisson's ratio (NPR) behaviour [1][2][3][4].It is well known that the re-entrant structure of auxetic materials results in NPR due to which these materials contract in all directions while compressed or stretched in all directions when extension is applied along one of their axes.These re-entrant auxetic topologies can be developed through thermo-mechanical, braiding, injection moulding and additive manufacturing methods, which is why the auxetic materials are also termed as auxetic metamaterials [5].These auxetic metamaterials have been found suitable to develop composites of enhanced mechanical resistance for stress resistance, vibration damping and shock energy absorption [6].The interest in using auxetic material is progressing in the direction of developing auxetic composites of various forms including auxetic cores in sandwich panels [7][8][9][10], auxetic geometries inclusions in polymeric matrix [11][12][13], auxetic tubes inclusions in polymeric foams [14,15], tubes with auxetic fillers [16,17] and polymer/foam filled auxetic structures [18,19].Another type of auxetic composites is auxetic cementitious composites (ACCs), in which auxetic materials in the form of additively manufactured auxetic geometries, foams or fabrics are embedded into a cementitious matrix [20,21].
ACC in the form of embedded auxetic foams into cementitious mortar matrix was first developed by Zahra and Dhanasekar [22].In this study, small-scale prismatic ACC samples were developed and tested under compression.The test results showed improvement in failure pattern by reducing the debonding and increased ductility as compared to glass fibre-reinforced cementitious composites.However, due to lower strength of auxetic foams, the overall strength of ACC samples was reduced by maximum 10%.Similar observations were made in [23].To overcome this issue, metallic auxetic meshes were developed by Kim et al [24,25] and were embedded in the cement matrix to make ACC samples, which were then characterised under uniaxial compression and tension.Strength enhancement and less brittle failure of composites was observed in the ACC samples developed by Kim et al [24,25].Similarly, braided composites were used in [26][27][28] to develop high strength and high NPR auxetic meshes for civil engineering strengthening applications.However, development of auxetic materials for embedment into ACC in the form of foams, metallic meshes and braided meshes was challenging due to non-availability of manufacturing facilities of these auxetic forms at a wider scale.
Asad et al [29] developed ACC beams by embedding a fabric made of auxetic yarn [30] into cementitious mortar matrix and tested under flexural loading.The behaviour of auxetic fabric embedded ACC beams was compared with carbon fibre reinforced polymer fabric embedded beams and enhanced energy absorbing and high ductility was noted for the ACC beams.The application of these ACC in impact resistance of walling structures was studied numerically by the same authors in [31], where it was noted that ACC application has enhanced flexural performance and energy absorption of walls under lateral impact loading.Nevertheless, auxetic textiles are also not widely available, which is a hinderance in their wider application.Additive manufacturing of auxetic metamaterials is an alternative option, which has opened opportunities of their applications in ACC.However, research in additively manufactured ACC has only been started recently and is slowly evolving [21].
Rosewitz et al [32] used architected cement-polymer composites by embedding various 3D printed polymerbased honeycomb geometries including auxetic geometries into the cementitious matrix.It was reported that the reentrant auxetic embedded composites performed well in terms of strength and ductility under compression and flexural loads.Some researchers [33,34] have also attempted to develop the cellular cementitious composites (CCCs) by moulding the cementitious mortar mix into cellular structure by casting them into 3D printed cellular shaped silicone moulds.These composites were tested under compression and NPR was observed for the auxetic CCCs, which was further studied numerically in [35,36].However, brittle failures were observed in those studies due to the absence of reinforcement.In another research [37], a cellular cementitious composite was manufactured through 3D printing of mortar mix.However, it was concluded that large scale manufacturing of these composites will need further research.
Recently, further advancement has been made by few researchers by filling cementitious mortar mix [38] or concrete [39,40], into metallic auxetic honeycomb structures, which were tested under compression for the confining effects on cementitious mortar/concrete provided by the auxetic lattices.The auxetic cellular tubes and honeycombed structures provided effective confinement to concrete under compression.Zhou et al [41] used metallic auxetic honeycombed structures filled with foam concrete to test under low velocity impact loading; the results revealed that the constraint provided by auxetic honeycomb on foam concrete resulted in efficient energy absorption.An auxetic foam coated, concrete filled steel composite was tested numerically in [42] for effective damping of seismic waves to less than 10 Hz.Barri et al [43] have developed a conducive metamaterial concrete by filling it into 3D printed polymer auxetic lattices which performed well under cyclic compression load with an ability to conduct electricity for their application in smart civil infrastructure.Chen et al [44] studied the static and dynamic compressive behaviour of 3D printed auxetic lattice reinforced ultra-high-performance concrete (UHPC) and reported that auxetic lattices increased the energy absorption characteristics of UHPC with enhanced performance due to confining effect of lattices.The above research proves growth in ACCs development.
Additively manufactured auxetic reinforcement in the form of mesh or bars for enhancing the flexural capacity of cementitious matrix has been researched scarcely.Xu et al [45] manufactured 3D printed auxetic mesh as circular bars and embedded them into cementitious mortar matrix for making ACC beams.Polymer material was chosen for 3D printing to avoid corrosion caused in metallic reinforcement in conventional beams and re-entrant auxetic geometry was selected for high energy absorption and ductility enhancement of the ACC beams.The ACC beams showed high energy absorption capacity under four-point flexural loads.Polymeric auxetic reinforcement in the form of flat rectangular meshes can also be used for enhancing the out-of-plane (OOP) flexural capacities and energy absorption of the cementitious composite panels for protective applications.
In this research, 3D printed re-entrant chiral auxetic (RCA) geometries developed earlier by Zahra [5] were embedded into cementitious mortar matrix to develop ACC panels of small scale.This research is an important milestone in the development of additively manufactured 'tuneable' construction materials of high energy absorption characteristics, which can be altered according to the need for protective application in civil engineering.The main contribution of this paper is advancement in the understanding of flexural behaviour of cementitious composites embedded with 3D printed auxetic meshes, which is a predominant response for structures under extreme loads.The details of manufacturing and characterisation of ACC panels tested under flexural loading are presented.Two different polymer materials were used to print the auxetic meshes and two different types of pre-mix mortar matrices of low and high strength were employed to make the ACC panels.In addition, geometrical parameters were also differed to investigate its effect on the mechanical behaviour of ACC.

Characterisation of RCA mesh
The RCA geometries developed in Zahra [5] were employed in this research to manufacture ACC composites by embedding into cementitious mortar matrices.The design and printing of RCA meshes, mechanical properties of printing materials, and OOP flexural test results of printed RCA meshes to find the best orientation in terms of strength and stiffness are discussed in the following sub-sections.

RCA mesh geometrical design and printing
A typical single cell of the designed RCA geometry is shown in figure 1(a).Three different geometrical dimensions namely RCA-1, RCA-2 and RCA-3 were adopted to study the effects of changing geometries on the OOP flexural behaviour of the RCA geometries and the ACC composites.The re-entrant angle (θ) for all the geometries was 30 • , while radius (r) and thickness (t) were 1.5 mm and 2 mm, respectively for all the RCA geometries.The height (h), length (L) and distance (d) were differed for the three geometrical variations as mentioned in figure 1(a).The geometries were printed in horizontal and vertical orientations as shown in figures 1(b) and (c) to investigate the impact of cell orientation in the longitudinal axis of the geometries.The differences in lengths and widths were due to different cell dimensions used.The best orientation was selected based on the test results of individual geometries under OOP flexural loading.The extruded thickness of geometries in both orientations was kept as 10 mm for their suitability as embedded meshes in the ACC composites.
The RCA geometries were printed in poly-lactic acid (PLA) and thermoplastic polyurethane (TPU) filaments with 3 mm and 2 mm diameters, respectively, as per the requirement of available printer having 0.5 mm nozzle and layer resolution of 0.05 mm-0.4 mm.The printing layer height was 0.2 mm, and the speed of printing was 30 mm s −1 .It must be mentioned that the filaments were deposited parallelly to the flexural load direction as mentioned in figures 1(b) and (c) for all the meshes.The change in the direction of filament deposition will affect the mechanical properties under flexure, which were not investigated in this paper.The mechanical properties of PLA and TPU materials were also evaluated under tension and compression according to ASTM D 638 [46] and ASTM D 695 Testing and stess-strain properties of printing materials.[47], respectively.Conventional dog-bone shaped specimens of size 40 mm (width) × 100 mm (length) × 10 mm (thickness) were used for tensile tests, whereas prismatic samples of size 25 mm (width) × 50 mm (length) × 25 mm (thickness) were made by 3D printing as shown in figures 2(a) and (b), respectively.Three similar samples were printed and tested to measure the variability in the test results.The testing was carried out using an INSTRON machine with a 50 kN load cell capacity at a displacement rate of 1 mm min −1 .Digital image correlation (DIC) was adopted to analyse the deformation of the specimens.A monochrome camera was employed on a fixed tripod to capture the images of samples at the rate of 10 frames per second.The samples were speckled using a black marker for accuracy in correlating the grey images for the displacement and strain evaluation.More details on the application of DIC for material characterisation using similar cameras and DIC technique can be seen in [5,22,48].The mean compressive strength of PLA print was 83.5 MPa with a coefficient of variance (COV) of 2.8% and of TPU print was 83.8 MPa with a COV of 3.6%.Both materials showed similar strength characteristics, the PLA and TPU samples failed in similar manner, due to excessive bulging in lateral direction caused by tensile strains.The mean tensile strength of PLA and TPU were determined as 41.6 MPa (COV 4.5%) and 3.8 MPa (COV 6.7%), respectively.The strength of TPU was much lower than the PLA printed sample due to its softness as reported in a previous study [49].
Using the DIC data, stress-strain curves were plotted for the PLA and TPU materials under compressive and tensile loading conditions.The average compressive and tensile stress-strain plots are shown in figures 2(c) and (d), respectively.It can be observed clearly that both materials had similar compressive strengths with different deformation characteristics.As expected, TPU being flexible polymer, behaved similar to soft polymeric materials with lower stiffness and extended plastic behaviour as marked in figure 2(c) with a densification behaviour shown after around the strain level of 0.25 (mm mm −1 ).Whereas the behaviour of PLA had limited plasticity with peak stress reached at 0.035 (mm mm −1 ) under compression and at 0.0086 (mm mm −1 ) under tension.After peak, there was some plasticity behaviour exhibited until final failure at the stain of 0.128 (mm mm −1 ) under compression and at 0.035 (mm mm −1 ) strain in tension.These stress-strain responses are important for theoretical as well as numerical modelling of the RCA structures for future studies.The elastic moduli of PLA were 3300 MPa (COV 2.8%) and 5532 MPa (COV 3.4%) in compression and tension, respectively.While for TPU, these were computed as 113.7 MPa (COV 3.2%) and 53.5 MPa (COV 4.5%) correspondingly under compressive and tensile tests.

Testing of printed RCA meshes under OOP flexural loading
The printed RCA specimens shown in figures 1(b) and (c) were tested under OOP flexural loads using the same testing machine that was used for the PLA and TPU material testing.
A uniform displacement at the rate of 1 mm min −1 was applied to ascertain the flexural strength and load-displacement characteristics.A total of 36 specimens were tested which consisted of three (3) similar samples for each type and orientation of RCA geometries under three-point flexural loads.The testing scheme for RCA meshes is given in table 1 and the test set-up is shown in figure 3.
For differentiating and referring the RCA mesh samples, an alpha-numeric nomenclature was used as given in table 1.The first three letter showed the printing material (PLA or TPU), the next three letter represent RCA geometry followed by a numeric digit showing the three types of geometrical shapes (1, 2, 3).The last three letters show the orientation of cells vertical (Ver) and horizontal (Hor).The span (L) between the support reactions as marked in figure 3 (and given in table 1) differed for each RCA meshes due to different cell sizes.The bottom supports on either side of load was on the middle of two cells, which changes the span lengths.However, to make a meaningful comparison, moment capacities of meshes were compared instead of loading capacity.Since bending moment is a multiple of load and span length, it would counter the effect of different spans and loads.Similar to material tests, DIC method was employed to measure the surface strains on all the tested RCA meshes.The meshes were speckled randomly using the black marker as shown in figure 3 for accuracy in the correlation results.

Flexural test results of printed RCA meshes
The experimental results were analysed in terms of failure patterns, OOP moment-displacement relationships and flexural characteristics of the tested RCA meshes.The displacement profiles and patterns were evaluated using the analysis of digital images through a DIC software.The vertical displacement occurred at mid-span, which was measured through DIC software and was normalised by dividing it with the span of meshes to cater for different span lengths.The OOP moment capacity vs. displacement/span ratio plots for each RCA mesh type were then developed.The moment capacity was preferred over the OOP loading for making a meaningful comparison between the tested RCA meshes of varied cells, overall width and span lengths.Figure 4 shows typical failure pattern of all RCA meshes.The failure in PLA-RCA1/2/3-Ver meshes (figure 4(a)) occurred due to excessive opening of gap at the mid-span of meshes on the tension side.Few PLA-RCA1/2/3-Ver meshes showed cracking and breaking of cell ribs closer to mid-span.The maximum mid-span displacement varied from 4 mm to 6 mm for these meshes.
The failure mode of PLA-RCA1/2/3-Hor meshes was flexible as compared to the vertical cell geometries and due to absence of gaps between the cells, all types of RCA mesh exhibited high displacement levels with ductile flexural behaviour.The ultimate failure occurred due to cracking and breaking of few cell ribs and drop of peak load by at least 20%.The ultimate displacement was around 30 mm for PLA-RCA1-Hor and more than 40 mm for PLA-RCA2/3-Hor meshes.
The behaviour of tested TPU-RCA1/2/3-Ver and TPU-RCA1/2/3-Hor meshes under OOP flexural are shown in figures 4(c) and (d), respectively.Despite having same sizes and cell geometries, the TPU meshes behaved widely different  to PLA meshes due to difference in their material properties.As shown in figure 4(c), all vertically oriented TPU-RCA meshes showed opening of gap between the cells at the ultimate stage.RCA1 mesh had denser cell design with minimum gap between the vertical cells of around 0.7 mm, which restricted the gap opening under flexure as compared to RCA 2 and RCA 3 meshes which had larger gap (1.3 mm and 2 mm) between the cells.The denser cell geometry enabled RCA1 meshes to densify under flexure after about 30 mm displacement at mid-span.
The OOP moment vs. displacement/span ratio relationship of PLA meshes is shown in figure 5.The PLA-RCA1-Ver mesh exhibited a prominent initial kink in the momentdisplacement/span ratio relationship which was due to separation of cells which get connected during 3D printing due to smaller gaps between the individual cells as shown in figure 5(a).The meshes then hardened under OOP loading until reaching peak, after which capacity reduced in the post peak range due to excessive opening in the mid-span and finally failing due to breaking of cell ribs at some locations.RCA 1 meshes showed high stiffness and flexural capacity as compared to RCA 2 and RCA 3 meshes.
Horizontally oriented PLA-RCA1/2/3-Hor meshes showed higher moment capacities as compared to the RCA meshes with vertical cell orientation as shown in figure 5(b).The flexural capacity of each type of RCA mesh was increased by 17.5% on an average.This behaviour is in agreement with the results reported in [50] who tested RCA geometries of horizontal and vertical cell orientations under tension and observed that the horizontal cell RCA geometries performed superior to vertically oriented cells RCA geometries.The higher ductility of PLA-RCA1/2/3-Hor meshes is obvious from the higher displacement/span ratio magnitudes which are 4 times higher than their vertically celled counterparts.
The moment vs. displacement/span ratio relationships for TPU meshes are shown in figure 6. Due to densification behaviour, the RCA1 meshes showed the highest moment capacity as compared to RCA2 and RCA3.RCA2 meshes showed insignificant densification in contrast to RCA1 meshes.RCA2 and RCA3 meshes, both vertical (figure 6 The peak OOP load (P) for all the tested RCA meshes were obtained from the raw data of testing machine as listed in table 2 and the corresponding ultimate flexural capacity for each mesh was calculated using the mechanical formula PL/4 for three-point bending (flexure) tests.The span (L) for each mesh are already provided in table 1. RCA1 consistently showed higher moment capacity than RCA2 and RCA3 meshes in both horizontally and vertically oriented cells.The average increase in moment capacity of PLA-RCA1 (Ver and Hor) meshes was about 1.2 folds as compared to PLA-RCA2 and 1.4 folds as compared to RCA3 meshes which can be considered marginal.However, for TPU-RCA1 (Ver and Hor) meshes the increase of moment capacity was about 15 folds when compared to RCA2 meshes and 27 folds when compared to RCA3 meshes.This wide difference in TPU meshes behaviour was due to dense cell geometry of RCA1 mesh, which densified under flexural load as can be seen from the moment-displacement/span ratio curves shown in figures 5 and 6.The highest moment capacity was found for TPU-RCA1-Hor mesh, which was 1.5 times greater than the PLA-RCA1-Hor mesh.
Table 2 also lists the ultimate displacement/span ratio of each tested mesh.The ultimate displacement was characterised as the displacement in post peak range for PLA meshes when the load dropped by at least 20%.Whereas, for TPU meshes, it was the ultimate densification displacement (for RCA1) or ultimate plastic displacement (for RCA2 and RCA3), when the testing machine had to be stopped for safety reasons as these meshes were tended to deform indefinitely.As discussed earlier, PLA meshes were less flexible, especially the vertical cell-oriented geometries and failed at lower displacement by opening of mid-span gap.Horizontally oriented meshes, on the other hand, underwent large mid-span displacement both for PLA and TPU meshes.Additionally, RCA2 and RCA3 had higher flexibility and showed larger mid-span displacement than RCA1 meshes.With increasing cell sizes, the displacement capacity of meshes increased as given in table 2.
Another important property, which was ascertained from the moment-displacement curves was the energy absorption by the RCA meshes under flexural loading.The energy absorption by each mesh was determined by computing the area under the load-displacement curve until ultimate point.The corresponding energy absorption values derived are given in table 2. These values were normalised by diving them with the cross-sectional area of each mesh to find the effective energy absorption in kJ m −2 .PLA-RCA1-Hor mesh exhibited the largest energy absorption of 44.9 kJ m −2 , followed by PLA-RCA2-Hor mesh with 40.8 kJ m −2 and 35.8 kJ m −2 for TPU-RCA1-Hor.These results concluded that the horizontal cell RCA meshes outperformed the vertical cell RCA meshes in terms of moment capacity, displacement capacity and energy absorption capacity.Therefore, for making ACCs only horizontal cell geometries (both PLA and TPU) were employed.
3D printed auxetic lattices have been tested by many researchers earlier under flexure however, those results cannot be directly compared with the results presented here due to their auxetic cell orientation and auxetic behaviour in the OOP direction.Whereas, the tested RCA meshes have auxetic behaviour in their planar direction.In a recent paper, Hamrouni [51] have developed anti-trichiral core from PLA/Flax filaments with auxetic behaviour in planar direction and tested them in three-point bending.Although different in material properties due to introduction of Flax  fibres, their flexural load-displacement curves were similar to PLA-RCA meshes tested in this paper.However, the maximum OOP load was reported as 275 N, which is lower than what was obtained in this paper.The previous tests on planar TPU auxetic mesh is not available in the literature for comparison.

Manufacturing and flexural testing of ACC specimens
In total, 42 ACC samples were developed by embedding the tested RCA meshes (PLA-RCA 1/2/3-Hor and TPU-RCA1/2/3-Hor) into two different types of pre-mix cementitious mortar mixes to test under OOP flexure.In making the ACC samples, two mortar mixes were made targeting low and high strength (i.e.compressive strength) mortars for rendering purposes.The sizes and number of the manufactured samples are given in table 3. The low strength mortar matrix was designated as LM, while HM represents high strength mortar.The compressive strength of both types of mortars was determined by testing standard 50 mm (diameter) × 100 mm (height) cylindrical samples according to AS 1012.9 [52].The average compressive strength of LM and HM was determined as 6.1 MPa (COV = 12.1%) and 41.4 MPa (COV = 10.6%)respectively.These two mortars were selected to study the influence of mortar strength on the flexural behaviour of ACC samples.The plain mortar samples were also moulded into prismatic shapes to test their flexural tensile strength, shown as LM-0 and HM-0 in table 3.
The ACC samples were casted into prismatic shapes using aluminium moulds.The low and high strength premix cement-sand mortar powder was mixed with the required quantity of water to make wet mortar matrix.The moulds were greased first and then the mortar matrix was poured into the moulds.The printed RCA meshes were then embedded into the matrix by pressing inside.The top of the samples was then levelled using spatula as shown in figure 7(a).The samples were dried for 24 h, thereafter the moulds were removed.All samples were wrapped into plastic sheets to cure into air at an ambient temperature of 20 ± 5 • C and relative humidity of 50%-60% in the lab for a period of 28 d as shown in figure 7(b).After curing, the samples were tested under flexural loading as shown in figure 7(c).Similar to RCA mesh tests, three-point loading set-up was employed with a span length of 100 mm.Despite different dimensions of ACC samples, the span distance for all the samples was kept same for simplicity.The samples were loading under displacement control at the loading rate of 1 mm/min in a 50 kN capacity hydraulic servo INSTRON machine.The DIC method was employed to capture images at every one second, which were later analysed to find the displacement and failure modes of the tested ACC samples.

Flexural test results of ACC specimens
The test results of ACC samples under flexure were analysed for their failure patterns, flexural moment-displacement response, and other characteristics including ultimate flexural capacity, ductility and energy absorption.

Failure pattern of ACC specimens
The specimens were tested until they failed by excessive cracking in mortar or when the peak load was dropped by at least 20%.Typical failure pattern at this failure stage for all types of samples tested are shown in figure 8.As expected, the failure of plain mortar sample was brittle in nature and the sample was ruptured into two pieces as soon as the peak load was reached.The crack pattern in plain mortar sample just before rupture is shown in figure 9(a).This brittle failure was observed due to weak tensile strength of cementitious mortar [32].
The ACC samples irrespective of mortar type (LM or HM) were failed in a ductile manner with enhanced displacement capacity.However, there was a considerable difference between the failure of ACC made of PLA-RCA1/2/3 meshes and TPU-RCA1/2/3 meshes.The samples that were made of hard polymer meshes PLA, showed multiple wider cracks on tension side of samples as marked in figures 8(b) and (c).These multiple cracks coalesced at the edges and resulted in brittle spalling of mortar pieces as the load increased.On close examination, it was also noted that there were cracks in PLA meshes.This behaviour can be attributed to lower ductility (by about 10 times) of PLA meshes in comparison to TPU meshes.On the other hand, only single crack was developed on the tension face of ACC samples embedded with TPU meshes as marked in figures 9(b) and (c).It can also be clearly observed that TPU meshes did not crack or stretched and maintain their elasticity even after failure of mortar.Due to this behaviour, all ACC samples with TPU meshes remain intact and did not exhibit mortar spalling or brittle collapse.This failure behaviour was consistent in LM and HM mortars and in all RCA meshes (RCA1, RCA2, RCA3).However, low strength mortar failed at an earlier stage as compared the high strength mortar.Similarly, the ductility levels were different for various RCA meshes, which is analysed in more detail in the upcoming sections.

OOP moment capacity vs. displacement/span ratio response of ACC specimens
The loading from the machine was converted into flexural moment by using the basic mechanics formula PL/4 for simply supported beam, with P being the load, L is span, which was 100 mm for all samples.The vertical displacement of all samples was measured using DIC analysis.The flexural moment vs. displacement/span ratio curves for the plain mortar LM and HM samples are shown in figure 9. High strength mortar HM had higher flexural capacity as well as larger displacement capacity under flexure.The average peak moment capacity of LM samples was 8700 N mm and corresponding modulus of rupture (or flexural strength) of 2.17 MPa.Whereas, the HM samples exhibited average flexural capacity of 33 000 N mm with corresponding flexural strength of   8.25 MPa which is about 3.8 folds higher than LM samples.The curves were mostly linear until peak, after which the samples ruptured in a brittle manner into two pieces.The displacement capacity of HM samples was also 1.8 times higher than LM samples.
Figures 10(a) and (b) shows the flexural capacity vs. displacement/span ratio curves of ACC samples made of LM mortar embedded with PLA-RCA and TPU-RCA meshes.The plain mortar curves are also shown for comparison.In PLA-RCA composites, the initial cracking (first peak) in mortar was at a very low displacement which was same as plain mortar sample.After initial cracking, the PLA meshes started to take flexural stress and these ACC samples continued to take load under in-elastic range until reached their second peak or ultimate moment capacity at a higher displacement level (at least 16 folds).The intermediate dips in the flexural load-displacement curves show crack propagation or multiple cracks development in mortar.After reaching peak, the load gradually dropped until failure, which was due to cracking in PLA meshes.The initial stiffness of all ACC with different types of PLA-RCA meshes is mostly same, however, RCA1 showed the highest moment capacity, which was followed by RCA2 and RCA3.This can be attributed to high flexural strength of RCA1 meshes as compared to RCA2 and RCA3 meshes as discussed in section 2.3.
The LM-TPU-RCA composites as shown in figure 10(b) exhibited enhanced ductility which is obvious from the displacement/span ratio levels reaching close to 1.The specimens showed first peak at a smaller displacement level which was similar to plain mortar strength (LM-0), after which the load dropped by 4 times due to cracking in mortar.At this point, TPU meshes started to take the flexural load until reaching a second peak at a very high displacement level (at displacement/span ratio of 0.5).The softness or low stiffness of TPU is expected to contribute to this behaviour.Despite low stiffness (by around 100 times), the TPU meshes outperformed PLA meshes in terms of ductility.However, for both PLA and TPU meshes, not significant enhancement of flexural capacity was observed when compared to control plain LM mortar sample.
It must be mentioned that the shape of flexural capacity curves with sudden drop in the capacity after first peak is similar to as reported in previous studies for ACC samples tested under compression [33] and flexural load [29].However, due to difference in material properties, no direct comparison is possible.
Figure 11 shows the moment-displacement/span ratio response of HM-RCA composites.The behaviour of HM-PLA-RCA was quite similar to LM-PLA-RCA composites, however, the failure occurred at a relatively lower displacement/span ratio (∼ 0.25).The RCA1 mesh composites showed the highest flexural capacity as compared to RCA2, RCA3 and plain HM mortar samples (as shown in figure 11(a)).This behaviour is consistent in all the ACC samples tested due to denser cell geometries of RCA1 meshes.The moment dropped after first peak due to initial cracking of mortar, when PLA meshes started to take flexural loads until reaching the ultimate moment capacity, which was followed by cracking in PLA meshes which resulted in the final failure of ACC samples.HM-TPU-RCA composites behaved similar to their LM counterparts, except the moment capacity was five folds higher especially for TPU-RCA1 meshes as shown in figure 11(b).The TPU-RCA3 meshes did not contributed to flexural capacity which can be seen with a lowest first peak in their moment capacity-displacement/span ratio curve.The load drop was significant after initiation of cracking in mortar due to softness (lower stiffness) of TPU meshes.However, they started to take the flexural stresses and second peak was observed at a high displacement/span ratio of 0.5.The loading was stopped when this ratio became closer to 1 for safety reason.

Flexural characteristics of ACC specimens
The flexural characteristics of the tested ACC samples were determined from the moment capacity and displacement responses presented in the previous section and the key parameters derived are listed in table 4. The peak load and corresponding ultimate moment capacity were determined from the peak loading and span length (100 mm).The embedment of PLA and RCA meshes marginally enhanced the flexural resistance of ACC made of LM.The maximum increase was for LM-PLA-RCA1 composite, which was 11% higher than plain LM.Whereas, for HM samples, the HM-TPU-RCA1 composite showed about 40.5% enhancement in its flexural capacity as compared to the plain HM samples.However, the flexural capacity was decreased for RCA3 meshes due to larger cell geometries for both LM-PLA/TPU and HM-PLA/TPU composites.The benefit of dense RCA cell geometry is obvious from these results for enhanced flexural resistance.
The cracking displacement (shown in table 4) was found from the DIC analysis, when the first crack was initiated in the samples.The ultimate displacement was corresponding to the failure point which was considered at 20% drop of the peak load in the ACC samples made of PLA-RCA meshes.Whereas, for TPU-RCA reinforced ACC, the ultimate was considered when the load application was stopped for the safety of machine, since the load was kept on increasing for these ACC specimens.The ductility for these ACC samples can be measured in terms of ratio of ultimate vs. cracking displacement.The composites with PLA-RCA meshes exhibited ductility ratios in the range of 18-38, while for the TPU-RCA composites this ratio was ranged from 80 (LM-TPU-RCA1) to 1250 (HM-TPU-RCA3).The increase in ductility for RCA2 and RCA3 meshes was due to larger cell geometries that enables larger flexibility in bending of meshes and composites.However, the flexural strength was compromised for these bigger cells meshes.
The energy absorption of the ACC specimens was determined by taking the area under the load-displacement curves until ultimate failure point.The last column of table 4 shows the computed energy absorption values of the samples tested.For meaningful comparison, the effective energy absorption per unit area of ACC samples was determined.The energy absorption was lowest for LM-PLA-RCA meshes (2168-3700 kJ m −2 ), which was at maximum 44 times higher than the plain LM sample.The HM-TPU-RCA composites outperformed other ACC samples in terms of energy absorption which was ranged from 8775 kJ m −2 to 14 700 kJ m −2 .The results showed that the best performance in terms of flexural strength, ductility and energy absorption under OOP flexural loading was observed for HM-TPU-RCA1.The failure pattern of ACC with 3D printed RCA meshes was observed similar to previous studies conducted on auxetic lattices embedded in cementitious mortar by Rosewitz [32] and in terms of increased flexural strength and ductility.However, a direct comparison is not viable as the auxetic lattices designed in [32] had auxetic behaviour in OOP direction rather than in-plane direction as designed for RCA meshes in this paper.When compared to the flexural tests of beams in Asad et al [29], which were made by embedding auxetic fabric into mortar matrix, about six-times higher energy absorption values were achieved in RCA-TPU mesh composites.The flexural capacity for the ACC specimens tested in this paper is also higher (by 75%) than what was reported in [29].

Summary and conclusions
This paper presents the development and characterisation of cementitious composites embedded with RCA meshes as reinforcement under OOP flexure.Three different RCA reinforcing meshes (RCA1, RCA2, RCA3) having different cell geometries and orientation were manufactured through 3D printing using two polymer (PLA and TPU) filaments.These RCA meshes were tested under OOP flexural loads to study their flexural capacity, ductility and energy absorbing characteristics, where those testing enabled to select the best cell orientation of RCAs.The selected RCAs cell orientation were then used as reinforcing meshes into cementitious mortar matrix to increase its flexibility and energy absorption characteristics.Two types of mortar mixes with high and low compressive strength were employed to develop RCA embedded ACCs.The composites were then tested in OOP flexural loading to investigate the effectiveness of RCA meshes embedment into cement mortar.Following are the main conclusions from this study.
• The horizontal cell orientation for all three types of RCA1, RCA2 and RCA3 exhibited high flexural strength (by max 18% for PLA and 155% for TPU) and energy absorption (by max 280% for both PLA and TPU) under OOP flexural loading.The maximum energy absorption was 10.2 J for PLA-RCA1-Hor followed by 8 J for TPU-RCA1-Hor, where they were around four times higher than their corresponding vertical cell orientations.
• The RCA1 mesh irrespective of their printing material (PLA or TPU) showed the highest flexural capacity (maximum 25% for PLA and 96% for TPU) as compared to RCA2 and RCA3.This behaviour was mainly attributed due to denser cell geometry for RCA1 meshes, which resulted in densification under high OOP displacement.• The ACC embedded with RCA1 meshes also exhibited high flexural strength and energy absorption.Type of mortar and printing material for RCA meshes made major contribution in the performance of the developed ACC.High strength mortar with RCA1 mesh printed with TPU filament showed the highest flexural capacity 46.4 Nm with effective energy absorption of 14 700 kJ m −2 .• The ACC with PLA-RCA meshes showed relatively brittle failure pattern with multiple cracks in mortar and PLA mesh as compared to ACC with TPU-RCA meshes due to high flexibility and resilience of TPU meshes, where they enabled extensive bending of ACC with mostly single clean crack and no damage to TPU meshes.• The load-displacement characteristics of ACC with PLA-RCA meshes were seemed different from TPU-RCA meshes.After ACC reached its first peak, a sudden drop in the load was observed due to crack propagation in mortar which was higher for the TPU-RCA mesh composites due to their lower stiffness as compared to PLA-RCA mesh composites.A second load peak was then observed in both composites, which was followed by post-peak load drop in PLA-RCA composites at a lower displacement level.Whereas, TPU-RCA continued to densify at enhanced displacement levels, which enabled them to absorb more energy.
This research has extended the knowledge on OOP behaviour of 3D printed RCA meshes made of different polymers and their application as reinforcement in cementitious mortar matrices to make ACC.The benefits of using softer polymer TPU with a denser cell geometry (RCA1) performed best in energy absorption.However, the conclusions are based on limited tests carried on two types of mortar, three cell geometries and two different printing filaments.More studies are required for variety of mortar types, auxetic geometries and printing materials.In future, finite element modelling of 3D printed ACC will also be performed.The results of this paper will be important to validate those models and to further study the flexural response of these composites for different material and geometrical properties.

Figure 1 .
Figure 1.Designing and printing of RCA meshes.

Figure 2 .
Figure 2. Testing and stess-strain properties of printing materials.

Figure 4 .
Figure 4. Typical failure patterns of RCA meshes under OOP flexure loading.
(a)) horizontal (figure 6(b)) cell orientation due to wider spaces between their cell exhibited plastic behaviour as shown with an extended plastic plateau in their moment-displacement/span curves.Larger the cell geometry, greater was their flexibility and plasticity as can be seen from the large magnitudes of displacement/span ratios in figures 7(a) and (b) that reached closer to 1 for RCA2 and RCA3 meshes.

Figure 7 .
Figure 7. Manufacturing and testing of ACC samples.

Figure 8 .
Figure 8.Typical failure pattern of ACC samples under OOP flexure.

Figure 9 .
Figure 9. OOP bending moment capacity vs. displacement/span ratio curves of plain mortar sample.

Table 2 .
Results summary of OOP flexural tests of RCA.Values in parenthesis are coefficient of variance (COV) determined for mean values. *

Table 3 .
Testing scheme for OOP flexural tests of ACC samples.

Table 4 .
Results summary of OOP flexural tests of ACC samples.
*Values in parenthesis are coefficient of variance (COV) determined for mean values